Geometrical computer



June 10, 1952 w. G. PROCTOR 2,600,264

GEOMETRICAL COMPUTER Filed Feb. 27, 1945 IN V EN TOR. WARREN G. PROCTOR-Patentecl June 10, 1952 GEOMETRICAL COMPUTER Warren G. Proctor, Boston,Mass, assignor, by

mesne assignments, to the United States of. America as represented bythe Secretary ofuWar Application February 27, 1945, Serial No. 580,020

8 Claims.

The present invention relates in general to electrical apparatus andmore specifically to electrical computing apparatus for the solution oftriangles.

In many types of electrical apparatus used for range finding or gundirecting, a method is desirable whereby triangles may be solvedelectrically. A special case of this problem is the solution of righttriangles, and in particular the determination of the length of thehypotenuse of a right triangle, being given the lengths of the twosides.

A common method of electrically solving this problem is to provide twoalternating current voltages, which are proportional respectively to thelengths of the two given sides of the triangle. One of these voltages isthen shifted in phase by 90 and the two voltages are then applied tosome type of summing device, the output of which is proportional to thepeak amplitude of the vector sum of the two quadrature voltages, andhence proportional to the hypotenuse of the right triangle.

Former computers have employed two coils displaced 90 in space in sometype of phase shifting device using rotating coils. One object of thepresent invention therefore is to produce this phase shift statically,thus conserving space and reducing the complexity of the phase shiftingdevice.

One important problem in any type of phase shifting device is theelimination of frequency sensitivity. In other words, both the phaseshift and the output amplitude of the device must be kept relativelyindependent of the frequency of the incoming alternating current wave.Since a complete 90 phase shift is extremely difficult to obtain, somemethod should also be provided to compensate for this incomplete phaseshift since it introduces an error in the magnitude of the output of thesumming device. the present invention, therefore, are to provide meanswhereby both the phase shift and the gain of the phase shifting devicewill be kept constant, and means to compensate for the error introducedby incomplete phase shift.

In accordance with the present invention, there is provided aharmonic-free constant amplitude alternating current source, from whichare taken two outputs proportional respectively to the lengths of thetwo known sides of the triangle. One of these voltages is fed to a phaseshifter consisting of a diiferentiator and an integrator so connectedthat the combined gain of the two is relatively independent ofvariations in frequency of applied voltage and the output is Otherobjects of shifted approximately in phase with respect to the input.This output is fed through a pushpull arrangement to two detectors,While the other output from the alternating current source is fed to thesame two detectors through a parallel arrangement. The output of thesedetectors is then combined in such a way that the resultant voltage isproportional to the arithmetic mean of the two detector input voltages.This latter arrangement compensates for incomplete phase shift, and thedirect current voltage produced is then proportional to the length ofthe unknown side of the triangle being solved.

For a'further understanding of this invention together with otherobjects and. features thereof,

reference is had to the following detailed description taken inconnection with the accompanying drawings, in which:

Fig. 1.is a schematic diagram of one form of the invention; and

Fig. 2 is a vectordiagram showing phase relationships of some of thevoltages present in the apparatus.

Referring now more particularly to Fig. 1 of the drawings, there isprovided across terminals I0 and II a constant amplitude alternatingcurrent source, the output of which is free from harmonics of thefundamental frequency. This output is connected to two potentiometers,I2 and I4, each of which has in series with it a variable resistor, l6and I8, respectively. The variable tap of potentiometer 2 is connectedto the center tap A of the secondary of coupling transformer 20. Thevariable tap of potentiometer I4 is connected to the input circuits. ofthe two phase shifting triodes, 22 and 24. The input circuit of triode22 is an integrator composed of resistor 25 and capacitor 26, the latterbeing connected to the plate of triode 22 rather than to ground, thusintroducing a certain amount of negative feedback into the stage.

The input circuit of triode 24 is a differentiator composed of capacitor21 and resistor 28, the latter being coupled through capacitor 29 to theplate of triode 24, thus introducing negative feedback into this stage.Capacitor 29 is large enough to be a very low impedance to alternatingcurrent ofthe frequency used, and serves to block the D.-C. platevoltage of triode 24 from its grid. Theplates of triodes 22 and 24 areconnected respectively :to' the two ends of the primary of couplingtransformer 20, the center tap ofthe primary being connected to theplate supply voltage. Resistor 30 serves as a grid leak for triode 24,thus preventing the grid of this triode from being in a floatingcondition.

The two ends of the secondary of coupling transformer 20 are connectedrespectively to the grids of triodes 32 and 34, which are connected ascathode followers. The outputs of triodes 32 and 34 are connectedthrough coupling capacitors 35 and 36 to the plates of diode detectors38 and 40, respectively. Averaging resistors 4| and 42 are so connectedthat the direct voltage present at point B is the arithmetic mean of theoutput voltages of the two diodes, which in turn are. proportionalrespectively to the total inputs to the two cathode follower triodes.

When the circuit of Fig. l is in operation, thevariable tap ofpotentiometer I2 is adjusted so that the voltage applied to the centertap ofthe' secondary of transformer 20 is proportional to the length ofone known side of the triangle to be solved. Because of the center taparrangement this voltage is fed equally and in the same phase to thegrids of the two. cathode follower triodes 32 and 34.

Similarly, the variable tap of potentiometer I4 is adjusted so that thevoltage applied to the input circuits of the phase shfting triodes 22and 24, is proportional to the length of the other known side of thetriangle to be. solved. Because of the constants of the integrator inputcircuit consisting of resistor 25 and. capacitor 26, the current throughthis circuit is substantially in phase with the applied. voltage;however, the voltage across capacitor 26 issapplied to the grid oftriode 22, and this voltage lags the current in the circuit by 90, andhence. lags the applied voltage by approximately the same. amount-Similarly, the constants ofthe differentiatcr input circuit, consistingof capacitor 21 and resistor 28, cause the current through it to leadthe applied voltage by approximately 90.. The voltage across theresistor 28 is. applied to the. grid of triode 24, and: this voltage is.in phase with the current, and hence leads the applied voltage. byapproximately 90. Because of. these phase shifts, the two triodes 22 and24. are fedl80 out of phase with each other and hence operate push-pull,the. two push-pull output. voltages: each being. approximately 90 out ofphase with the input voltage to the phase shift circuit, one leading andone lagging.

The phase shifting circuits are claimed. in. my divisional application,Serial. No. 204,355, filed on November 1'7, 1950.

These push-pull voltages are fed through coupling transformer 20, sothat they appear in pushpull on the grids of triodes 32 and 34. At thesame time the voltage from the variable tap of potentiometer I2 ispresent on the grids of these triodes, and it is in quadrature with bothof the push-pull voltages. The resultant voltage on each grid,therefore, is the vector sumof the two quadrature voltages, and henceproportional to the length of the hypotenuse of the triangle to besolved. Since triodes 32 and 34 are identical, their outputs,neglecting. thev effect of. incomplete phase shift, will be equal. Theseoutputs are fed to identical diode rectifiers 38 and 40, the outputs ofwhich are respectively equal to the peak values of the inputs appliedfrom triodes 32 and 34. The outputs of diodes-38 and 40 are combinedthrough resistors 4| and 42 in such a manner that the voltage present atpoint B is equal to the arithmetic mean of the two diode outputs andagain is proportional to the length of the hypotenuse of the trianglebeing solved.

By properly choosing the turns ratio of coupling transformer 20 and thegain of triodes 22 and 24, the constant of proportionality between thelength of the one known side of the triangle and the magnitude of thepush-pull voltage fed to the grids of triodes 32 and 34 can be madeapproximately equal to the constant of proportionality between thelength of the other known side of the triangle and the magnitude of thevoltage fed to the grids of the same two triodes through the center tapof the secondary of coupling transformer 20. Minor adjustments to makethese constants more nearly equal can be made by varying. the.resistance of calibrating resistors I 6 and i8.

It can beshownby circuit analysis that the gain of the. integratorcircuit including triode 22, resistor 25, and capacitor 26 is roughlyinversely proportional to frequency, while the gain of thediiferentiator circuit including triode 24, capacitor 2.1,, and resistor28 is roughly directly proportional. to frequency. As a result, thecombined output of these triodes, which flows in the primary oftransformer 20, is substantially independent of frequency variations ofthe input signal. It can further be shown that if we choose as a'nominalfrequency that frequency at which the theoretical gain of the integratorcircuit and the differentiator circuit are equal, then variations offrequency of the order of ten per cent above and below this nominalfrequency will cause variations in output of the order of only one-halfper cent.

Referringnext to Fig. 2, we see a vector diagram of several of thevoltages present in the circuit. Vector R represents the alternatingvoltage fed. through the center tap of the secondary oftransformer 20:to the grids of triodes 32 and 34. Vectors H and H represent thepush-pull voltages fed to the same grids. If the phase shift of theintegrator and differentiator circuits were exactly H and H would beperpendicular to R. However, the actual phase shift is always somewhatless than 90, the actual amount varying with frequency. Therefore H andH are shown not perpendicular to R, the amount of divergence from theperpendicular being exaggerated however for ease of illustration.Vectors E and E are the resultant voltages present on the grids oftriodes 32 and 34..

Since a cathode follower stage changes only the magnitude and not thephase of a voltage fed through it, these same vectors may represent thevoltages fed to the two detector diodes 38 and 4.0; The output of thesediodes depends. not on the phase but only on the magnitude of the inputto them, and therefore their D.-C. output magnitudes may be representedby the lengths. of E and E1. The D.-C. output at. point B as hasbeenexplained isthe arithmetic mean of the detector outputs, and its.magnitude is shown. by

This can be seen to be approximately equal in magnitude to E", which iswhat the D.-C. output at B would have been if the phase shift had beenexactly 90. The double detector therefore can be seen to compensate forerrors introduced by incomplete phase shift.

While there has been described what is at present considered a preferredembodiment of the invention, it will be obvious to those skilled inthe-art that various changes and modifications may be made thereinwithout departing from the invention, and that values of circuitconstants given in the figures are illustrative only. It is aimed in theappended claims to cover all such changes as fall within the true scopeof the invention.

What I claim to have invented is:

1. In an electrical apparatus for the solution of right triangles, meansfor supplying two alternating computing voltages having magnitudesproportional respectively to the lengths of the two known sides of theright triangle being solved; static phase shifting means, including anintegrator circuit and a diiferentiator circuit, for producing from oneof said computing voltages two push-pull voltages each differing inphase by 90 from the input voltage to said phase shifting means; meansfor coupling said one of said computing voltages to the input of saidphase shifting means; at least two detecting means; means forsimultaneously coupling each of said push-pull voltages and the other ofsaid computing voltages to the input of a different one of saiddetecting means; and means associated with said detecting means forproducing a D.C. output which is equal in magnitude to the arithmeticmean of the outputs of said detecting means, and which is proportionalin magnitude to the length of the hypotenuse of the right triangle beingsolved.

2. In an electrical apparatus for the solution of right triangles, meansfor supplying two alternating voltages having magnitudes proportionalrespectively to the lengths of two known sides of a triangle, means forproducing two pushpull voltages each 90 out of phase with one of saidalternating voltages, means for combining the other of said alternatingvoltages with said push-pull voltages to produce two resultant voltages,at least two detector means, means for feeding said resultant voltagesto said detector means, resistor means connected to the output of saiddetector means, and an output means connected at an intermediate pointon said resistor means.

3. In an electrical apparatus for the solution of right triangles, meansfor providing two alternating voltages substantially in phase, havingmagnitudes proportional respectively to two sides of the triangle,static means, including an integrator circuit and a difierentiatorcircuit, for shifting the phase of one of said alternating voltagesapproximately 90 with respect to the other alternating voltage, asumming means the output of which is proportional to the hypotenuse ofthe triangle, and means for feeding both of said voltages to saidsumming means.

4. In combination an integrator circuit and a difi'erentiator circuithaving a common input and a common push-pull output, two detectors fedby said push-pull output, and having an additional input and a commonoutput.

5. In an electrical apparatus for the solution of right triangles, meansfor supplying two alternating voltages, one of said voltages having amagnitude proportional to the length of one known leg of a triangle, theother of said voltages having a pair of components in push-pullrelationship, each of said components proportional to the length of asecond known leg of said triangle and having a phase relation to saidfirst alternating voltage, means for combining said first alternatingvoltage with each of said push-pull voltage components to produce tworesultant voltages and means to determine the average magnitude of saidtwo resultant voltages.

6. An electrical apparatusvfor the solution of right triangles,comprising means for providing two alternating voltages substantially inphase, having magnitudes proportional respectively to two sides of thetriangle, a static phase shifter for shifting the phase of one of saidalternating voltages of approximately 90 with respect to the otheralternating voltage connected to be supplied from said providing means,said phase shifter including means therein for translating voltagesrespectively directly proportional and inversely proportional tofrequency to render said phase shifter independent of variation infrequency, a summing means the output of which is proportional to thehypotenuse of the triangle, and means for feeding both of said voltagesto said summing means, said feeding means comprising connectionsrespectively from said providing means and said phase shifter to saidsumming means.

7. An electrical apparatus for the solution of right triangles,comprising means for providing two alternating voltages substantially inphase, having magnitudes proportional respectively to two sides of thetriangle, a static phase shifter for shifting the phase of one of saidalternating voltages of approximately 90 with respect to the otheralternating voltage connected to be supplied from said providing means,said phase shifter including means therein for rendering the phase shiftproduced by said phase shifter independent of variation in frequency, asum ming means the output of which is proportionalto the hypotenuse ofthe triangle, and means for feeding both of said voltages to saidsumming means, said feeding means comprising connections respectivelyfrom said providing means and said phase shifter to said summing means.

8. An apparatus according to claim 7, wherein said summing meansincludes means for providing an output which is proportional to thearithmetic mean of the input voltages applied to said summing means.

WARREN G. PROCTOR.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 2,004,613 Meacham June 11, 19352,225,348 Mikelson Dec. 17, 1940 2,250,461 Batchhelder July 29, 19412,256,538 Alford Sept. 23, 1941 2,279,506 Reid Apr. 14, 1942 2,282,105Tunick May 5, 1942 2,375,227 Hillman May 8, 1945 2,382,994 Holden Aug.21, 1945 2,385,334 Davey Sept. 25, 1945 2,439,381 Darlington Apr. 13,1948 2,447,517 Manson Aug. 24, 1948 2,465,624 Agins Mar. 29, 1949

